DiSSECT

Name	w-255-mers
Category	nums
Description	Original nums curve from https://eprint.iacr.org/2014/130.pdf
Field	Prime (0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd03)
Field bits	255
Form	Weierstrass $y^{2} = x^{3} + a x + b$
Param $a$	0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd00
Param $b$	-0x51bd

Order	0x7fffffffffffffffffffffffffffffff864a38283ad2b3dfab8fac983c594aeb
Cofactor	0x1
$j$ -invariant	0x661734f09b8540109c7681cdde324ef2080bff3ca6ef898c0002ffb7060110ba
Trace $t$	0x79b5c7d7c52d4c2054705367c3a6b219
Embedding degree $k$	0x3fffffffffffffffffffffffffffffffc3251c141d6959efd5c7d64c1e2ca575
CM discriminant	-0x1c622a801d47d31929427898fe6049161ccb6472bd76d9816a4f91a0475ad2d9b

$cofactor ()$
order	0x7fffffffffffffffffffffffffffffff864a38283ad2b3dfab8fac983c594aeb
cofactor	0x1

$discriminant ()$
cm_disc	None
factorization	None
max_conductor	None

$twist_order (d e g = 1)$
twist_cardinality	0x8000000000000000000000000000000079b5c7d7c52d4c2054705367c3a6af1d
factorization	None

$twist_order (d e g = 2)$
twist_cardinality	0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd0239dd57fe2b82ce6d6bd8767019fb6e9e3349b8d4289267e95b06e5fb8a5bba75
factorization	None

$kn_factorization (k = 1)$
(+)factorization	['0x2', '0x2', '0xd', '0x3b', '0x1fe1', '0xb48b', '0x4a38bf89ed42039', '0x1a3780881d4886ea3ba35bc58d18547c2ff8cac7']
(+)largest_factor_bitlen	0x9d
(-)factorization	['0x2', '0x3', '0x3', '0x43', '0x9d', '0xb3', '0x2479', '0x681173', '0x44604a62c855bfe5e408585d7aee72b7d256d5ae08e72489b']
(-)largest_factor_bitlen	0xc3

$kn_factorization (k = 2)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	['0x17b', '0x58bf34df5b2371', '0x1f2cd1b9937efdfba0ee166128f33469a232a57eb44e5965f']
(-)largest_factor_bitlen	0xc1

$kn_factorization (k = 3)$
(+)factorization	['0x2', '0x47', '0x655', '0x1f14708cb', '0x498b7072d1', '0xc3ea7753e88ef71396824c0a8b0443303c1dd6c101']
(+)largest_factor_bitlen	0xa8
(-)factorization	['0x2', '0x2', '0x2', '0x2', '0x2', '0x2', '0x5', '0x5', '0x17', '0x8b', '0x13d', '0xb109b', '0xaaf7d9aa7', '0x1abb157f73b', '0x206b55777b741d', '0x28a915bd80a388c5f5f1']
(-)largest_factor_bitlen	0x4e

$kn_factorization (k = 4)$
(+)factorization	['0xb', '0x11', '0x4577', '0x1bc13', '0x7fce5', '0x10d8b79b09d', '0x4074630080e7b00528ed', '0x2bf386b39ad63fe35bd57']
(+)largest_factor_bitlen	0x52
(-)factorization	['0x3', '0x1d', '0x5e293205e293205e293205e293205e28d87d38060dd8caf10b7284d9eba8acd']
(-)largest_factor_bitlen	0xfb

$kn_factorization (k = 5)$
(+)factorization	NO DATA (timed out)
(+)largest_factor_bitlen	NO DATA (timed out)
(-)factorization	['0x2', '0x7', '0x2db6db6db6db6db6db6db6db6db6db6d8b63a65782b8f719066a2b5af0fb519d']
(-)largest_factor_bitlen	0xfe

$kn_factorization (k = 6)$
(+)factorization	['0xbe9', '0x1f1b', '0xaec83ae65', '0x38ef5c968c2a40dfa5', '0xda706c088d06f5b310c137538368c7f9']
(+)largest_factor_bitlen	0x80
(-)factorization	['0x5ad', '0x679', '0x139d', '0x5873', '0x1f2e5', '0xbd28f', '0x5d2e13', '0x4cadca8b5a56e698f', '0x13a683b287832701f2db55']
(-)largest_factor_bitlen	0x55

$kn_factorization (k = 7)$
(+)factorization	['0x2', '0x5', '0x29', '0x19e0d', '0x239a5', '0x4207db', '0x25aabe8a7697ecefba5dd7193d26ac0bd87b97c18da3d9cc9']
(+)largest_factor_bitlen	0xc2
(-)factorization	['0x2', '0x2', '0x3', '0xb', '0x1505', '0x18206ac3b', '0x65f326ff1', '0x89aa97a04383623b30c431edcfae55041932eb0361d']
(-)largest_factor_bitlen	0xac

$kn_factorization (k = 8)$
(+)factorization	['0x3', '0x3', '0x3', '0x3', '0x71', '0x155f', '0xe0bb9d', '0x281875f129c6d', '0x9bf35629b549624cbaadbf4d9527be9154d02cdf']
(+)largest_factor_bitlen	0xa0
(-)factorization	['0x5', '0x3d', '0x288d9f8af', '0x6a5a66563575', '0x57a50dcd1f23f', '0x9502d6f1a5a5b042f0f25def97665b']
(-)largest_factor_bitlen	0x78

$torsion_extension (l = 2)$
least	0x3
full	0x3
relative	0x1

$torsion_extension (l = 3)$
least	0x8
full	0x8
relative	0x1

$torsion_extension (l = 5)$
least	0x18
full	0x18
relative	0x1

$torsion_extension (l = 7)$
least	0x10
full	0x10
relative	0x1

$torsion_extension (l = 11)$
least	0x5
full	0x5
relative	0x1

$torsion_extension (l = 13)$
least	0xc
full	0xd
relative	0x1

$torsion_extension (l = 17)$
least	0x10
full	0x11
relative	0x1

$conductor (d e g = 2)$
ratio_sqrt	0x79b5c7d7c52d4c2054705367c3a6b219
factorization	['0x47', '0x1b6d78c0d981319b1dd86954ade4a9f']

$conductor (d e g = 3)$
ratio_sqrt	0x4622a801d47d31929427898fe6049161ccb6472bd76d9816a4f91a0475ad3692
factorization	['0x2', '0xfe7a9b03e105c71', '0x2346fcc9815477ceb8eebb005988a9faf72ef0cebb7a9f859']

$conductor (d e g = 4)$
ratio_sqrt	0x5e331295970aa8f55bbd8e8d531b01ab9143f70c02378162cb9c85ecb526a74f655cbddef32d3a898a8af0cedd65a38d
factorization	NO DATA (timed out)

$embedding ()$
embedding_degree_complement	0x2
complement_bit_length	0x2

$class_number ()$
upper	NO DATA (timed out)
lower	NO DATA (timed out)

$small_prime_order (l = 2)$
order	0x7fffffffffffffffffffffffffffffff864a38283ad2b3dfab8fac983c594aea
complement_bit_length	0x1

$small_prime_order (l = 3)$
order	0xe38e38e38e38e38e38e38e38e38e38e2b5d94763f6cbea7130ff6bb94ed7a1a
complement_bit_length	0x4

$small_prime_order (l = 5)$
order	0x2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa8218bd62be463bf5392fe432bec86e4e
complement_bit_length	0x2

$small_prime_order (l = 7)$
order	0x3fffffffffffffffffffffffffffffffc3251c141d6959efd5c7d64c1e2ca575
complement_bit_length	0x2

$small_prime_order (l = 11)$
order	0x3fffffffffffffffffffffffffffffffc3251c141d6959efd5c7d64c1e2ca575
complement_bit_length	0x2

$small_prime_order (l = 13)$
order	0x3fffffffffffffffffffffffffffffffc3251c141d6959efd5c7d64c1e2ca575
complement_bit_length	0x2

$division_polynomials (l = 2)$
factorization	[['0x3', '0x1']]
len	0x1

$division_polynomials (l = 3)$
factorization	[['0x4', '0x1']]
len	0x1

$division_polynomials (l = 5)$
factorization	[['0xc', '0x1']]
len	0x1

$volcano (l = 2)$
crater_degree	0x0
depth	0x0

$volcano (l = 3)$
crater_degree	0x0
depth	0x0

$volcano (l = 5)$
crater_degree	0x0
depth	0x0

$volcano (l = 7)$
crater_degree	0x0
depth	0x0

$volcano (l = 11)$
crater_degree	0x2
depth	0x0

$volcano (l = 13)$
crater_degree	0x1
depth	0x0

$volcano (l = 17)$
crater_degree	0x1
depth	0x0

$volcano (l = 19)$
crater_degree	0x0
depth	0x0

$isogeny_extension (l = 2)$
least	0x3
full	0x3
relative	0x1

$isogeny_extension (l = 3)$
least	0x4
full	0x4
relative	0x1

$isogeny_extension (l = 5)$
least	0x6
full	0x6
relative	0x1

$isogeny_extension (l = 7)$
least	0x8
full	0x8
relative	0x1

$isogeny_extension (l = 11)$
least	0x1
full	0x5
relative	0x5

$isogeny_extension (l = 13)$
least	0x1
full	0xd
relative	0xd

$isogeny_extension (l = 17)$
least	0x1
full	0x11
relative	0x11

$isogeny_extension (l = 19)$
least	0x14
full	0x14
relative	0x1

$trace_factorization (d e g = 1)$
trace	0x79b5c7d7c52d4c2054705367c3a6b219
trace_factorization	['0x47', '0x1b6d78c0d981319b1dd86954ade4a9f']
number_of_factors	0x2

$trace_factorization (d e g = 2)$
trace	0x79b5c7d7c52d4c2054705367c3a6b219
trace_factorization	['0x3', '0x907', '0xbe9', '0xf425', '0x15175', '0x1cd34d', '0x15836857fb5858b', '0x33a3811eff119fc3d8bfb5b494508bf']
number_of_factors	0x8

$isogeny_neighbors (l = 2)$
len	0x0

$isogeny_neighbors (l = 3)$
len	0x0

$isogeny_neighbors (l = 5)$
len	0x0

$q_torsion ()$
Q_torsion	0x1

$hamming_x (w e i g h t = 1)$
x_coord_count	0x75
expected	0x7f
ratio	1.08547

$hamming_x (w e i g h t = 2)$
x_coord_count	0x3fe9
expected	0x3f40
ratio	0.98967

$hamming_x (w e i g h t = 3)$
x_coord_count	0x14dac3
expected	0x14d63f
ratio	0.99915

$square_4p1 ()$
p	0x1
order	0x1

$pow_distance ()$
distance	0x79b5c7d7c52d4c2054705367c3a6b515
ratio	3.5786799867032686e+38
distance 32	0xb
distance 64	0x15

$multiples_x (k = 1)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 2)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 3)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 4)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 5)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 6)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 7)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 8)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 9)$
Hx	None
bits	None
difference	None
ratio	None

$multiples_x (k = 10)$
Hx	None
bits	None
difference	None
ratio	None

$x962_invariant ()$
r	0x260ad32bdc94c614c23b58d6abadef723c97eef8e0f7d98557a50870710bbd8b

$brainpool_overlap ()$
o	0x3ffffffffffffffffffffd01

$weierstrass ()$
a	0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd00
b	-0x51bd

Curve detail

Definition

Characteristics

Traits